Hi there. In this page, I play around with plotting random walk paths in the Python programming language. The code is heavily based from the book Data Analysis In Python by Wes McKinney. In the book, there is no code for the plots. I add in the code for plots.

This post can also be found on my website here.

Plotting A Single Random Walk Path

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To start off import random, numpy as np, seed from random and matplotlib's pyplot as plt.

import random
from random import seed
from matplotlib import pyplot as plt
import numpy as np

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Having a random seed allows for the results to be reproduced. Not having one will change the results and plots every time random functions are used.

# Set seed for reproducibility
seed(123)

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For simplicity, the random walk starts at the position of y = 0. The walk list will store the position of the random walk after each step/jump. The number of steps is 1000.

position = 0
walk = [position]
steps = 1000

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In a random walk, each jump either goes up by one or down by one. This jump is done with the use of an if-else statement in one line within the for loop. Each step is added to the random walk's position. The position can be viewed as the cumulative sum of all the random walk up and down jumps at a time point.

for i in range(steps):
    step = 1 if random.randint(0, 1) == 1 else -1
    position += step
    walk.append(position)

Plotting The Result

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Now that the random walk positions have been obtained after each step, a plot can be generated with matplotlib's pyplot. You can use plt.plot(walk) on its own but I wanted to add in some labels and a title.

# Plot results

plt.plot(walk)

plt.xlabel("\n Number Of Steps", size = 14)
plt.ylabel("Position \n", size = 14)
plt.title("Random Walk Plot \n", size = 20) 

plt.show()

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Multiple Random Walk Paths

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In the previous section, only one random walk path was generated. For multiple random walk paths, the code would need some adjustments.

In the code below, the number of random walk paths and the number of steps for each random walk are specified. Each random number is generated through Numpy's randint function (which is different from random's randint function). This random number is either a zero or one.

In the steps variable, any draws that are a 1 stay a 1 and anything other than a 1 turns into a -1 with the use of Numpy's where function. Recall that a 1 represents an up jump in the random walk and a -1 represents a down jump. The random walk positions are in the walks variable.

### Multiple Random Walks

nwalks = 200
nsteps = 100

draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1
steps = np.where(draws == 1, 1, -1)
walks = steps.cumsum(1)

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Plotting the results for multiple random walks is not much different than before in terms of the code.

# Plot results

plt.plot(walks)

plt.xlabel("\n Time", size = 14)
plt.ylabel("Position \n", size = 14)
plt.title("Multiple Random Walks Plot \n", size = 20) 

plt.show()